I used to sell NeXT software and hardware when working for a company called OpenSource (they actually owned the opensource.com domain name before RedHat got it).
At that time "open" meant interopable rather than the current "open source software" meaning. For instance, the DBkit and EOF database software could talk to Sybase or Oracle or any other database for which there was a driver.
As a result we used NeXTstations for all our tasks, and really, that was the best computing environment I have used. As another poster says, we really haven't "budged the needle" since Nextstep v3.3 of the OS.
Later while working for another company I got the ability to talk to Keith Ohlfs who designed the UI and personally thanked him for it.
My understanding is the use of Open was used before this by Symbolics and possibly other lisp machine manufactuers. I'd argue too that their systems were more open, where the user could read the system software and patch it in while it was running.
The foundations of the open source movement too stem from these communities (the GPL) not from NeXt. It would appear to me, like other Unix manufacturers, NeXt claimed openness when mostly it was marketing-speak for "based on Unix".
The word "open" at that time, when used in conjunction with Unix, meant something along the lines of "POSIX" compliant. Even earlier uses were more along the lines of "uses TCPIP and supports NFS" IIRC, though that is before my time.
Open as used above, was started by the users, not the OS vendors, in reaction to APIs that weren't portable between different versions of Unix - the vendors were trying to create lock-in and the users didn't like it. Even Microsoft NT supported POSIX (not sure how well it worked).
Definitely the open source movement came from outside NeXT... Gnu was already around and used a lot, in fact the GCC compiler, ported for Next was the supported C/ObjC/C++ compiler.
At that time "open" meant interopable rather than the current "open source software" meaning. For instance, the DBkit and EOF database software could talk to Sybase or Oracle or any other database for which there was a driver.
As a result we used NeXTstations for all our tasks, and really, that was the best computing environment I have used. As another poster says, we really haven't "budged the needle" since Nextstep v3.3 of the OS.
Later while working for another company I got the ability to talk to Keith Ohlfs who designed the UI and personally thanked him for it.